INTEGRODIFFERENTIAL EQUATIONS AND DELAY INTEGRAL-INEQUALITIES

In this paper sufficient conditions for the boundedness, asymptotic properties and exponential decay are first obtained for solutions of linear systems of integral inequalities with infinite delay. Then nonlinear integro-differential equations are reduced to delay integral inequalities by the variation of parameter formula, and some criteria are given for asymptotic stability, uniformly asymptotic stability and exponential asymptotic stability. The results obtained here are illustrated by examples which have been particularly difficult to treat by means of the standard Lyapunov theory.